Structure of Positive Radial Solutions of Semilinear Elliptic Equations

Abstract

We study the positive radial solutions of a semilinear elliptic equationΔu+f(u)=0, wheref(u) has a supercritical growth order for smallu>0 and a subcritical growth order for largeu. By showing the uniqueness of positive solutions behaving likeO(|x|2−n) at infinity, we give an almost complete description for the structure of positive radial solutions. As a consequence, we also prove the uniqueness of positive solutions of the nonlinear Dirichlet problem for the equation in a finite ball.